Lennard-Jones Devonshire equation of state

Equation of state discussed in these papers is given in this Volume under Detonation (and Explosion), Equations of State", as Lennard-Jones Devonshire Equation of State"... 

Detonation pressure may be computed theoretically or measured exptly. Both approaches are beset with formidable obstacles. Theoretical computations depend strongly on the choice of the equation of state (EOS) for the detonation products. Many forms of the EOS have been proposed (see Vol 4, D269—98). So.far none has proved to be unequivocally acceptable. Probably the EOS most commonly, used for pressure calcns are the polytropic EOS (Vol 4, D290-91) and the BKW EOS (Vol 4, D272-74 Ref 1). A modern variant of the Lennard Jones-Devonshire EOS, called JCZ-3, is now gaining some popularity (Refs -11. 14). Since there is uncertainty about the correct form of the detonation product EOS there is obviously uncertainty in the pressures computed via the various types of EOS ... 

Lennard-Jones Devonshire (LJD) Equations of State. For gases of low density, the following equation of LJD (Ref lb, p 55) applies ... 

Rankine-Hugoniot equations 181-87 (Equations of state which include among others the following Jones Miller, Lennard-Jones Devonshire, Halford-Kistiakowsky-Wilson, Joffe its modification by Su Chang, Taylor, Kihara Hikita, Travers, Cook, Kistiakowsky-Wilson-Brinkley and Polytropic equations) 194 (Landau-Stanyukovich and Hirschfelder et al equations of state 11) J.F. Roth, Explosiv-stoffe 1958, 50 (Abel sche Zustandsgleichung fur die Detonation) 12) Cook (1958), 37 (General equation of state) 62-3 [Halford-Kistiakowsky-W ilson-Brinkley equation of state, (listed as K-H-W-B equation of state)] ... 

CA 55, 24011(1961) (Equation of state of the products in. RDX detonation) Mj) W. Fickett, "Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermo-lecular Potentials , Los Alamos Scientific Laboratory Report LA-2712(1962), Los Alamos, New Mexico, pp 9-10 (Model of von Neumann-Zel dovich), pp 153-66 [Comparison of KW (Kistiakowsky-Wilson) equation of state with those of LJD (Lennard-Jones-Devonshire) and Constant-/ ] M2) C.L. 

Next to the - Chapman-Jouget theory, during the last 50 years, the principal methods of calculating detonation pressure and the velocity of flat detonation waves have been the Becker-Kistiakowsky-Wilson (BKW), the Lennard-Jones-Devonshire (LJD) and the Jacobs-Cow-perthwaite-Zwisler (JCZ) equations of state. 

The other cause, the density effect, is especially important at high densities, where molecules are more or less confined to cells formed by their neighbors. In analogy to the well-known quantum mechanical problem of a particle in a box, the translational energies of such molecules are quantized, and this has an effect on the thermodynamic properties. In 1960 Levelt Sengers and Hurst [3] tried to describe the density quantum effect in term of the Lennard-Jones-Devonshire cell model, and in 1980 Hooper and Nordholm proposed a generalized van der Waals theory [4]. The disadvantage of both approaches is that, in the classical limit, they reduce to rather unsatisfactory equations of state. 

Except for oxygen-balanced expls, the computation of detonation products depends strongly on the choice of the equation of state (EOS) for these products. In the US the BKW EOS (see Vol 4, D272-R) has been favored and most of the computed product compns below will be based on it. Some of these will be compared with the relatively few calcns based on a Lennard-Jones-Devonshire (UD) EOS (see Vol 4, D287-L) CJ state product compns calcd via the BKW EOS are compared with compns computed with LJD types of EOS in Tables 2—4. For PETN (Table 2) an early variant of the LJD EOS (Ref 1) shows no solid C in the products and somewhat more CO than the BKW computation. Note that for PETN both EOS give product compn that show relatively little variation with p q, the initial density of the expl. This is not the case for RDX and TNT (Tables 3 4) where a change in Pq results in substantial changes in product compn. 

The van der Waals equation of state can be replaced by better models of the liquid state, for example, the gas of hard spheres with intermolecular attractions superimposed (78), or the Lennard-Jones and Devonshire (19) theory of liquids. 

The most successful equation of state for semicrystalline polymers such as PE and PA stems from two unlikely sources (1) calculation of 5 = a of polymeric glasses at T< 80K [Simha et al., 1972] and (2) the Lennard-Jones and Devonshire (L-JD) cell model developed originally for gases and then liquids. Midha and Nanda [1977] (M-N) adopted the L-JD model for their quantum-mechanical version of crystalline polymers, taking into account harmonic and anharmonic contributions to the interaction energy. Simha and Jain (S-J) subsequently refined their model and incorporated the characteristic vibration frequency at T= 0 K from the low-Tglass theory [Simha and Jain, 1978 Jain and Simha, 1979a,b] ... 

Equations of state derived from statisticai thermodynamics arise from proper con-figurationai partition functions formuiated in the spirit of moiecuiar modeis. A comprehensive review of equations of state, inciuding the historicai aspects, is provided in Chapter 6. Therefore, we touch briefly in oniy a few points. Lennard-Jones and Devonshire [1937] developed the cell model of simple liquids, Prigogine et al. [1957] generalized it to polymer fluids, and Simha and Somcynsky [1969] modified Pri-gogine s cell model, allowing for more disorder in the system by lattice imperfections or holes. Their equations of state have been compared successfully with PVT data on polymers [Rodgers, 1993]. 

Using the theory of Lennard-Jones and Devonshire for the description of the liquid state, De Boer and Lunbeck have calculated Pci and Pj at various values of v and T. Their expression of the reduced equation of state differs from (V-21) only by the fact that Aes is replaced by A. 

Simple Cell Model of Prigogine et al. The cell model by Frigogine et al. (10-12) is an extension of the cell model for small molecules by Lennard-Jones and Devonshire (68) to polymers. Each monomer in the system is considered to be trapped in the cell created by the surroimdings. The general cell potential, generated by the smroimdings, is simplified to be athermal. This turns the simple cell model into a free volmne theory. The mean potential between the centers of different cells are described by the Lennard-Jones 6-12 potential. The dimensionless equation of state has the following form ... 

Careri (Ref 7b) suggested a procedure for computing exactly the thermodynamic functions of a nonequilibrium system. The state of the system was then varied, at fixed volume and temperature, so as to give a minimum Helmholz free energy, consistent with such conditions as are imposed to permit the exact computation. The condition under which this method leads to self-consistent equations is discussed in detail. The method is then applied in a way that is very close to the Lennard-Jones and Devonshire cell method, bur with cells of variable size. The distribution within a cell is assumed to be Gaussian. Mayer Careri claimed that the method is easier to apply than the cell method, but it seems to be rather complicated... 

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